Cold wallet are the best way to secure your Bitcoins because they cannot be accessed.
Once you transfer your keys to the cold storage , only transfer what you need to your hot wallets.
Also,
Firstly yes the cold storage are regarded as the most secure means of storing your bitcoin simply because your keys do not get access to the internet of at all they are setup well. But that doesn’t mean they can get access to them, you still need to secure the device and most importantly the seed phrase or private key well. Should any one get hold of you seed phrase back up then they can simply get access to the wallet.
1, the best way to secure your keys is to combine cold and hot wallet uses so that only the cryptocurrency you need at the moment is in the connected wallet.
I agree with you that little amounts for daily spending can still be kept on hot wallets, but it seems you’re confusing the word connecting both. You can simply use a hot wallet to track transactions of your cold wallet in a watch only mode and also use to create an unsigned transaction and also to broadcast a signed transaction also.
2, cold wallet, also called cold storage the best way to secure your Bitcoins private keys .
I can’t agree less but the best method again is how you back it up offline, do not leave them laying on cold storage device only, the device can maybe run into problems and you will need a backup to recover your wallet. Back your keys up offline in two to three different places
3, some exchange provide institutional_level secure cold data storage for user's kes, but some critics advise against this method.
You call them critics? I don’t, stay off centralized exchanges that promise to secure your funds for you, be your own bank by going for self custodial wallet